What are PCI and PCI Express slots used for?

PCI/PCI-Express (aka PCI-E) slots let you install expansion cards.

Expansion cards give your computer additional capabilities. Some very common expansion cards were sound cards, 56k modems, and Ethernet adapters. You don't have to populate your PCI/PCI-E slots, but it is an option if you need to extend your hardware.

Since the introduction of the PC in the early 1980's, more and more capability has been included on the motherboard. Most motherboards today include sound capability and (sometimes multiple) Ethernet ports.

The card must match the slot, e.g. if you have PCI-E slots, you need to buy a PCI-E card. Newer slots support faster hardware. PCI-E is the newest and fastest. PCI is still very common and included in motherboards. Older slot types include EISA (black) and AGP (brown - for graphics cards only).

No one makes RAM for PCI/PCI-E slots, RAM has had its own dedicated slim slot type on motherboards for about 20 years now (in the ISA days you could buy memory boards that plugged into the ISA slots). Hard drive "cards" were a short experiment in the early 80's and no longer are made. Hard drive controller cards are common though - these are just cards that sport additional IDE or SATA ports and let you attach more drives - but you need separate power lines for the drives off your power supply and you're responsible for having a case that lets you put them somewhere.

Both PCI and PCI-E have "mini" versions for laptop use.

On a modern system especially as a server of some sort, you can get by without any at all - You can go with onboard video (avoiding the use of a PCI-E slot for video card), ethernet (so you don't need a expansion slot for it either) and so on. Most modern boards are practically self contained.

As far as a home server system goes, I can see PCI-E slots used for a card that supports additional sata ports (assuming you had space and sufficient power in your case). I'd note that many MATX cases might not support the full 6 drives that the board could handle - most i've seen handle 2+2 or 3+2.

If cost was no object you can throw in a SSD or even ram on a PCI-E port. Both these act as expensive but INSANELY FAST storage options. Considering you're using a matx board, i'm assuming throwing a grand into very fast storage is not an option you're looking at, so lets ignore these.

If your server also does some form of routing which is common, you could also throw an additional network card (PCI-E for gig-e, PCI for 10/100). I often use ethernet as a simple fast way to transfer files directly from system to system as well. Having wireless is another possibility in that role.

With an MATX board you can't expect too many cards - you'd have one x16 (for a video card) and up to 3 other slots as per the specifications. On the other hand, in this role, nearly everything you need is built in, as I stated - I'd look at other specifications in deciding.